sensors

Article

Flow Control in Wells Turbines for HarnessingMaximum Wave Power

Jon Lekube 1,2,* ID , Aitor J. Garrido 1, Izaskun Garrido 1, Erlantz Otaola 1,3 and Javier Maseda 1

1 Automatic Control Group (ACG), Institute of Research and Development of Processes,Faculty of Engineering, University of the Basque Country (UPV/EHU), 48013 Bilbao, Spain;aitor.garrido@ehu.eus (A.J.G.); izaskun.garrido@ehu.eus (I.G.); erlantz.otaola@idom.com (E.O.);ispmaref@ehu.es (J.M.)

2 Promotion and Subsidies Area, Basque Energy Agency (EVE), Urkixo Zumarkalea, 36, 48011 Bilbao, Spain3 Advanced Design and Analysis (ADA), IDOM Consulting, Engineering and Architecture,

48015 Bilbao, Spain* Correspondence: jon.lecube@ehu.eus

Received: 29 December 2017; Accepted: 7 February 2018; Published: 10 February 2018

Abstract: Oceans, and particularly waves, offer a huge potential for energy harnessing all over theworld. Nevertheless, the performance of current energy converters does not yet allow us to usethe wave energy efficiently. However, new control techniques can improve the efficiency of energyconverters. In this sense, the plant sensors play a key role within the control scheme, as necessarytools for parameter measuring and monitoring that are then used as control input variables to thefeedback loop. Therefore, the aim of this work is to manage the rotational speed control loop inorder to optimize the output power. With the help of outward looking sensors, a Maximum PowerPoint Tracking (MPPT) technique is employed to maximize the system efficiency. Then, the controldecisions are based on the pressure drop measured by pressure sensors located along the turbine.A complete wave-to-wire model is developed so as to validate the performance of the proposedcontrol method. For this purpose, a novel sensor-based flow controller is implemented based on thedifferent measured signals. Thus, the performance of the proposed controller has been analyzed andcompared with a case of uncontrolled plant. The simulations demonstrate that the flow control-basedMPPT strategy is able to increase the output power, and they confirm both the viability and goodness.

Keywords: wave energy; sensing applications; power management; energy harvesting; Wellsturbines; Mutriku power plant

1. Introduction

Sensors have been widely used in power generation plants during the last centuries. The mainrole of most of the sensors has been the continuous monitoring of the plant parameters, until recentyears. However, some concerns regarding plant security or the need of efficiency improving makesensors essential component within the control system. In addition, renewable energy systems, and inparticular marine energy systems, must face new challenges in terms of operation and maintenance(O&M). According to a recent report from the European Union, the annual O&M costs of ocean energydevices can be as high as 5.8% of capital expenditures. In this context, the use of sensors will helpmitigate O&M expenses and anticipate failures.

The potential of marine energy as a source of electricity generation is widely recognized [1–5].Compared to the approximately 29% currently representing renewable energies in the Europeanenergy supply, the challenge of the sector is to increase this percentage to more than 60%. In thissense, wave energy is still situated in the first grade of development, with most devices in TRL 3–4 [6].The divergence of the technology has slowed down the progress of these devices, not yet being capable

Sensors 2018, 18, 535; doi:10.3390/s18020535 www.mdpi.com/journal/sensors

Sensors 2018, 18, 535 2 of 15

of competing with other conventional and unsustainable energy sources [7]. Nevertheless, the firstprototypes have shown optimistic results in terms of feasibility and efficiency.

In this paper an Oscillating Water Column-based wave energy system is presented. This kind ofdevices represents a consolidated group within the ocean energy harnessing systems [8,9]. There existseveral facilities based on the same principle that have been put into operation in recent years. Figure 1shows the Mutriku Wave Power Plant, located in the Atlantic coast of the Basque Country. It stands asthe first wave power plant composed by more than one turbine and connected to the power grid [10].It is important to point out that the Atlantic coast offers great possibilities for harnessing waveenergy [11,12]. Nowadays the power plant is used as a testing laboratory, where the Basque EnergyAgency (EVE) offers the possibility to test large variety of components, for example, turbines or evencontrol methods. The plant is included together with other projects, such as the Biscay Marine EnergyPlatform (BIMEP), inside the MaRINET2 project, which joins different testing facilities dedicated towave energy systems development. Due to its experimental functionality, a large number of sensorsare installed along the power plant. Among these sensors stand Oscillating Water Column (OWC)chamber sensors, turbine pressure drop sensors, vibration, temperature or water level sensors.

Sensors 2018, 18, x 2 of 14

capable of competing with other conventional and unsustainable energy sources [7]. Nevertheless,

the first prototypes have shown optimistic results in terms of feasibility and efficiency.

In this paper an Oscillating Water Column-based wave energy system is presented. This kind of

devices represents a consolidated group within the ocean energy harnessing systems [8,9]. There

exist several facilities based on the same principle that have been put into operation in recent years.

Figure 1 shows the Mutriku Wave Power Plant, located in the Atlantic coast of the Basque Country.

It stands as the first wave power plant composed by more than one turbine and connected to the

power grid [10]. It is important to point out that the Atlantic coast offers great possibilities for

harnessing wave energy [11,12]. Nowadays the power plant is used as a testing laboratory, where

the Basque Energy Agency (EVE) offers the possibility to test large variety of components, for

example, turbines or even control methods. The plant is included together with other projects, such

as the Biscay Marine Energy Platform (BIMEP), inside the MaRINET2 project, which joins different

testing facilities dedicated to wave energy systems development. Due to its experimental

functionality, a large number of sensors are installed along the power plant. Among these sensors

stand Oscillating Water Column (OWC) chamber sensors, turbine pressure drop sensors, vibration,

temperature or water level sensors.

Figure 1. View of the Mutriku Wave Power Plant built at Atlantic coast of the Basque Country [EVE].

The main limitation of OWC devices using Wells turbines is imposed by the stalling

phenomenon, which produces severe loses in the generated power at low rotational speeds.

Therefore, some research has focused on optimizing Wells turbines to avoid negative behavior and

to improve their aerodynamics response [13–17]. Nevertheless, novel advanced control methods are

needed to make the technology profitable [18–22]. In this context, the Maximum Power Point

Tracking (MPPT) control method pursues the objective of optimizing the energy conversion.

Although MPPT has already been successfully implemented in other renewable energy systems

such as photovoltaic or wind, marine energy systems and in particular OWC devices require a deep

study of this control strategy with the aim of adapting it to the new environment [23,24].

This article is organized as follows: Section 2 presents a model of OWC devices. In Section 3 the

characteristics of sensors and network topology are described. Section 4 implements the control

strategy that maximizes the power extraction in OWC devices. The implementations performed for

the representative case studies so as to verify the proper operation of the control scheme proposed in

this paper were carried out in Section 5. Finally, some conclusions are given in Section 6, that end the

manuscript.

2. OWC Modeling

In this section, the main parameters taking part in OWC motion, namely airflow velocity,

pressure drop and mechanical torque among others, are defined. In this sense, Wells turbine-based

OWC device has been modeled by means of the aforementioned parameters and its performance has

been described.

Figure 1. View of the Mutriku Wave Power Plant built at Atlantic coast of the Basque Country [EVE].

The main limitation of OWC devices using Wells turbines is imposed by the stalling phenomenon,which produces severe loses in the generated power at low rotational speeds. Therefore, someresearch has focused on optimizing Wells turbines to avoid negative behavior and to improve theiraerodynamics response [13–17]. Nevertheless, novel advanced control methods are needed to makethe technology profitable [18–22]. In this context, the Maximum Power Point Tracking (MPPT) controlmethod pursues the objective of optimizing the energy conversion. Although MPPT has already beensuccessfully implemented in other renewable energy systems such as photovoltaic or wind, marineenergy systems and in particular OWC devices require a deep study of this control strategy with theaim of adapting it to the new environment [23,24].

This article is organized as follows: Section 2 presents a model of OWC devices. In Section 3the characteristics of sensors and network topology are described. Section 4 implements the controlstrategy that maximizes the power extraction in OWC devices. The implementations performed forthe representative case studies so as to verify the proper operation of the control scheme proposedin this paper were carried out in Section 5. Finally, some conclusions are given in Section 6, that endthe manuscript.

2. OWC Modeling

In this section, the main parameters taking part in OWC motion, namely airflow velocity, pressuredrop and mechanical torque among others, are defined. In this sense, Wells turbine-based OWC devicehas been modeled by means of the aforementioned parameters and its performance has been described.

Sensors 2018, 18, 535 3 of 15

The working principle of OWC devices is simple [25]. The incoming wave produces air compressionwithin the chamber when the water column is moved towards the top of the chamber. This air-pressure issupposed to produce enough airflow through the turbine duct to make the Wells turbine rotate, as it canbe seen in Figure 2. The same action occurs when the wave recedes. The vacuum produced within theOWC chamber during the wave recession produces the same airflow in the opposite direction.

Sensors 2018, 18, x 3 of 14

The working principle of OWC devices is simple [25]. The incoming wave produces air

compression within the chamber when the water column is moved towards the top of the chamber.

This air-pressure is supposed to produce enough airflow through the turbine duct to make the Wells

turbine rotate, as it can be seen in Figure 2. The same action occurs when the wave recedes. The

vacuum produced within the OWC chamber during the wave recession produces the same airflow

in the opposite direction.

Figure 2. Working principle of Oscillating Water Column (OWC)-based devices.

The airflow velocity crossing the turbine duct can be studied by means of Airy’s theory [26].

There exist adaptations of this theory that consider the combination of regular waves so as to

facilitate the study of these systems [27–29]. According to the aforementioned process, the airflow

velocity at the inlet of the turbine can be estimated as

tTcT

l

D

awctvt

2cossin

8)(

2 ,

(1)

being a the wave amplitude, T the period and c the speed. Besides, w is the width and l the length of

the OWC chamber and D the diameter of the turbine duct.

Despite the bidirectional airflow generated during a wave period, the turbo-generator system is

able to keep the same rotational direction by using Wells turbines, as it also occurs with impulse

turbines [30]. This kind of turbines, usually known as self-rectifying turbines, always rotate in the

same direction regardless the airflow produced by incoming and outgoing waves. Nevertheless,

Wells turbines offers very poor efficiencies at low rotational speeds. This behavior is known as stall.

Since the turbine response varies at different rotational speeds, there exists a need to define a

dimensionless parameter that relates the rotational speed with airflow velocity determined in (1).

This parameter is known as flow coefficient, φ, and the relationship between both parameters is

given by the following equation:

t

t

r

v

(2)

Where tv is the air flow velocity (m/s), r is the radius of the turbine blade and t is the turbine

rotational speed (rad/s).

By means of the flow coefficient it may also be estimated the torque coefficient, Ct, and power

coefficient, Ca. Both parameters are empirically obtained and stand for own features of Wells

turbines. Furthermore, the peak appearing in the torque coefficient is a distinctive feature of Wells

turbine which produces the stalling behavior since the torque applied by the turbine drops

gradually as the value of the flow coefficient increases above 0.3. Ct and Ca are represented in Figure

3a,b, respectively.

Figure 2. Working principle of Oscillating Water Column (OWC)-based devices.

The airflow velocity crossing the turbine duct can be studied by means of Airy’s theory [26].There exist adaptations of this theory that consider the combination of regular waves so as to facilitatethe study of these systems [27–29]. According to the aforementioned process, the airflow velocity atthe inlet of the turbine can be estimated as

vt(t) =8awcπD2 · sin

πlcT

cos2π

Tt, (1)

being a the wave amplitude, T the period and c the speed. Besides, w is the width and l the length ofthe OWC chamber and D the diameter of the turbine duct.

Despite the bidirectional airflow generated during a wave period, the turbo-generator systemis able to keep the same rotational direction by using Wells turbines, as it also occurs with impulseturbines [30]. This kind of turbines, usually known as self-rectifying turbines, always rotate in thesame direction regardless the airflow produced by incoming and outgoing waves. Nevertheless,Wells turbines offers very poor efficiencies at low rotational speeds. This behavior is known asstall. Since the turbine response varies at different rotational speeds, there exists a need to definea dimensionless parameter that relates the rotational speed with airflow velocity determined in (1).This parameter is known as flow coefficient, ϕ, and the relationship between both parameters is givenby the following equation:

ϕ =vt

r · ωt(2)

where vt is the air flow velocity (m/s), r is the radius of the turbine blade and ωt is the turbine rotationalspeed (rad/s).

By means of the flow coefficient it may also be estimated the torque coefficient, Ct, and powercoefficient, Ca. Both parameters are empirically obtained and stand for own features of Wells turbines.Furthermore, the peak appearing in the torque coefficient is a distinctive feature of Wells turbine whichproduces the stalling behavior since the torque applied by the turbine drops gradually as the value ofthe flow coefficient increases above 0.3. Ct and Ca are represented in Figure 3a,b, respectively.

Sensors 2018, 18, 535 4 of 15Sensors 2018, 18, x 4 of 14

(a) (b)

Figure 3. Turbine characteristic curves. (a) Torque coefficient vs. flow coefficient; (b) Power

coefficient vs. flow coefficient. Dashed line: experimental curve. Solid line: approximated curve.

The curves in Figure 3 are composed by different points along the φ values according to

experimental results. However, they can produce discontinuities in the turbine response. Hence, in

order to smooth the response and to facilitate the analytical handling of the model, Ct and Ca have

been approximated by the following mathematical expressions [31]:

4

0

1

6

0

1

i

i

i

i

i

i

t

q

p

C

,

(3)

where, p1 = −0.001398, p2 = 0.01456, p3 = 0.1408, p4 = −0.7687, p5 = 0.9818, p6 = −0.202, and q1 = −0.06988, q2

= −0.3182, q3 = 0.06089, q4 = 1, and

75.475.1825 23

aC (4)

The responses of (3) and (4) have been represented with solid lines in Figure 3a,b, respectively.

In case of (4), it has only been calculated within the operating range so as to simplify the

mathematical expression.

The pressure drop along the turbine can be defined as

221tt

t

aa rva

KCdP (5)

being 2/nblK ta , where ρ is the air density (kg∙m−3), b is the width (m) and lt is the length (m) of

turbine blades, n is the number of blades, and ta is the surface of the turbine duct (m2).

Similarly, the mechanical torque developed by the turbine can be written by means of the

following expression:

22

ttatt rvrKCT , (6)

where r is the turbine tip radius (m).

3. Plant Sensors

The plant controller usually makes decisions based on the signals coming from different

sensors. In this sense, sensors contribute all the necessary inputs to the control system. There exist

many sensors that are used in marine environment to measure a wide range of parameters [32,33]. In

this particular case, in order to achieve the proposed objectives OWC chamber pressure and the

pressure drop along the turbine have been measured by means of pressure sensors. Figure 4 shows

two of the many sensors installed along the wave power plant of Mutriku.

Figure 3. Turbine characteristic curves. (a) Torque coefficient vs. flow coefficient; (b) Power coefficientvs. flow coefficient. Dashed line: experimental curve. Solid line: approximated curve.

The curves in Figure 3 are composed by different points along the ϕ values according toexperimental results. However, they can produce discontinuities in the turbine response. Hence,in order to smooth the response and to facilitate the analytical handling of the model, Ct and Ca havebeen approximated by the following mathematical expressions [31]:

Ct =

6∑

i = 0pi · φi−1

4∑

i = 0qi · φi−1

, (3)

where, p1 = −0.001398, p2 = 0.01456, p3 = 0.1408, p4 = −0.7687, p5 = 0.9818, p6 = −0.202, andq1 = −0.06988, q2 = −0.3182, q3 = 0.06089, q4 = 1, and

Ca = −25 · φ3 + 18.75 · φ2 + 4.75 · ϕ (4)

The responses of (3) and (4) have been represented with solid lines in Figure 3a,b, respectively.In case of (4), it has only been calculated within the operating range so as to simplify themathematical expression.

The pressure drop along the turbine can be defined as

dP = CaKa1at

(v2

t + (r · ωt)2)

(5)

being Ka = ρbltn/2, where ρ is the air density (kg·m−3), b is the width (m) and lt is the length (m) ofturbine blades, n is the number of blades, and at is the surface of the turbine duct (m2).

Similarly, the mechanical torque developed by the turbine can be written by means of thefollowing expression:

Tt = CtKar(

v2t + (r · ωt)

2)

, (6)

where r is the turbine tip radius (m).

3. Plant Sensors

The plant controller usually makes decisions based on the signals coming from different sensors.In this sense, sensors contribute all the necessary inputs to the control system. There exist manysensors that are used in marine environment to measure a wide range of parameters [32,33]. In thisparticular case, in order to achieve the proposed objectives OWC chamber pressure and the pressuredrop along the turbine have been measured by means of pressure sensors. Figure 4 shows two of themany sensors installed along the wave power plant of Mutriku.

Sensors 2018, 18, 535 5 of 15

Sensors 2018, 18, x 5 of 14

(a) (b)

Figure 4. Pressure sensors installed in wave power plant of Mutriku. (a) OWC chamber static

pressure sensor; (b) Wells turbine pressure drop sensor [EVE].

The OWC chamber pressure sensor (see Figure 4a) consists of PTX 7355 type Druck sensor. The

sensor provides 4–20 mA output signal with 15-bit output resolution. It is able to measure pressures

up to +/‒ 1 bar g, relative pressure, recorded by the plant Supervisory Control and Data Acquisition

(SCADA) every 100 ms.

The pressure sensor that measures the pressure drop along the turbo-generator system has two

meters, one at the inlet of the turbine and the second at the top of the module, as can be seen in

Figure 4b. In addition to this sensor, a static pressure sensor has also been installed at the top of the

module. The two pipes may be seen just at the top of the module in Figure 4b. The pressure drop

sensor consists of CMR controls P-sensor for low air pressure. It also provides 4–20 mA output

signal with 15-bit output resolution. The sensor might measure pressures up to +/‒ 3 kPa every 100

ms.

The data from the sensors is collected by a Beckhoff system, which turns both analog signals into

fieldbus signals. The connection between Beckhoff and Programmable Logic Controller (PLC) is

carried out by CTNet network of Control Techniques. CTNet fieldbus is a 5 Mbit Token Ring network

that supports peer-to-peer communications. Finally, the SCADA is connected to the PLC by means of

an OLE for Process Control (OPC) server/client configuration. Figure 5 shows the network topology

used to collect data from sensors.

Figure 5. Data collection network topology.

Figure 4. Pressure sensors installed in wave power plant of Mutriku. (a) OWC chamber static pressuresensor; (b) Wells turbine pressure drop sensor [EVE].

The OWC chamber pressure sensor (see Figure 4a) consists of PTX 7355 type Druck sensor.The sensor provides 4–20 mA output signal with 15-bit output resolution. It is able to measurepressures up to +/− 1 bar g, relative pressure, recorded by the plant Supervisory Control and DataAcquisition (SCADA) every 100 ms.

The pressure sensor that measures the pressure drop along the turbo-generator system has twometers, one at the inlet of the turbine and the second at the top of the module, as can be seen inFigure 4b. In addition to this sensor, a static pressure sensor has also been installed at the top of themodule. The two pipes may be seen just at the top of the module in Figure 4b. The pressure dropsensor consists of CMR controls P-sensor for low air pressure. It also provides 4–20 mA output signalwith 15-bit output resolution. The sensor might measure pressures up to +/− 3 kPa every 100 ms.

The data from the sensors is collected by a Beckhoff system, which turns both analog signalsinto fieldbus signals. The connection between Beckhoff and Programmable Logic Controller (PLC) iscarried out by CTNet network of Control Techniques. CTNet fieldbus is a 5 Mbit Token Ring networkthat supports peer-to-peer communications. Finally, the SCADA is connected to the PLC by means ofan OLE for Process Control (OPC) server/client configuration. Figure 5 shows the network topologyused to collect data from sensors.

Sensors 2018, 18, x 5 of 14

(a) (b)

Figure 4. Pressure sensors installed in wave power plant of Mutriku. (a) OWC chamber static

pressure sensor; (b) Wells turbine pressure drop sensor [EVE].

The OWC chamber pressure sensor (see Figure 4a) consists of PTX 7355 type Druck sensor. The

sensor provides 4–20 mA output signal with 15-bit output resolution. It is able to measure pressures

up to +/‒ 1 bar g, relative pressure, recorded by the plant Supervisory Control and Data Acquisition

(SCADA) every 100 ms.

The pressure sensor that measures the pressure drop along the turbo-generator system has two

meters, one at the inlet of the turbine and the second at the top of the module, as can be seen in

Figure 4b. In addition to this sensor, a static pressure sensor has also been installed at the top of the

module. The two pipes may be seen just at the top of the module in Figure 4b. The pressure drop

sensor consists of CMR controls P-sensor for low air pressure. It also provides 4–20 mA output

signal with 15-bit output resolution. The sensor might measure pressures up to +/‒ 3 kPa every 100

ms.

The data from the sensors is collected by a Beckhoff system, which turns both analog signals into

fieldbus signals. The connection between Beckhoff and Programmable Logic Controller (PLC) is

carried out by CTNet network of Control Techniques. CTNet fieldbus is a 5 Mbit Token Ring network

that supports peer-to-peer communications. Finally, the SCADA is connected to the PLC by means of

an OLE for Process Control (OPC) server/client configuration. Figure 5 shows the network topology

used to collect data from sensors.

Figure 5. Data collection network topology. Figure 5. Data collection network topology.

Sensors 2018, 18, 535 6 of 15

Data recorded by both sensors in comparison with the water level within the OWC chamber ispresented in Figure 6. This example of data corresponds to a period of 15 min collected on 10 October2017, starting at 6:00 a.m.

Sensors 2018, 18, x 6 of 14

Data recorded by both sensors in comparison with the water level within the OWC chamber is

presented in Figure 6. This example of data corresponds to a period of 15 min collected on 10

October 2017, starting at 6:00 Am.

Figure 6. OWC chamber water level and data recorded by pressure sensors installed in wave power

plant of Mutriku on 10 October 2017, 6:00 Am.

Previously, a thorough analysis has been carried out by the authors with the aim of developing

and establishing the OWC chamber modeling [26]. In that case the model was validated using a

20-min series of wave surface elevation data, collected every 2 h with a sampling period of 0.5 s. Using

a Workhorse 600 kHz from Teledyne RDI radar sensor, also known as Acoustic Doppler Current

Profiler, high frequency orbital velocities close to the surface were measured. From these

measurements, the data used to validate the OWC chamber model were derived.

4. Sensor-Based Flow Control MPPT Strategy

This section describes the control strategy proposed in this manuscript. As has been mentioned

before, the objective pursued in this paper consists in the output power maximization by means of a

MPPT strategy. This control technique has already been implemented in other renewable energy

generation plants, such as wind or solar energy, with successful results. Therefore, in case of wave

energy, MPPT should offer similar performance as in already implemented energy systems.

However, this strategy must be adapted to wave environment since the behavior of the parameters

to be controlled vary slightly from other systems.

The authors already presented a speed control-based MPPT strategy in [31]. However, in that

case the optimum rotational speed was empirically obtained from simulations and curve fitting

tools. The current research works provides enough mathematical background to display how the

optimum rotational speed is obtained.

As it happens in most energy systems where the main motion is the rotational movement of the

turbo-generator shaft, the performance of the system can steeply drop according to the rotational

speed and turbine characteristics. Therefore, in this particular case, MPPT strategy will basically

make use of the rotational speed control of the turbo-generator.

However, the expression of the optimum rotational speed must be obtained first. In this sense,

Equation (6) has been rewritten so as to obtain the mechanical power expression in terms of the

torque ratio to the rotational speed.

22

tttatt rvrKCP . (7)

Thus, Equation (7) may be derived with respect to the rotational speed, ωt:

Figure 6. OWC chamber water level and data recorded by pressure sensors installed in wave powerplant of Mutriku on 10 October 2017, 6:00 a.m.

Previously, a thorough analysis has been carried out by the authors with the aim of developingand establishing the OWC chamber modeling [26]. In that case the model was validated using a 20-minseries of wave surface elevation data, collected every 2 h with a sampling period of 0.5 s. Using aWorkhorse 600 kHz from Teledyne RDI radar sensor, also known as Acoustic Doppler Current Profiler,high frequency orbital velocities close to the surface were measured. From these measurements,the data used to validate the OWC chamber model were derived.

4. Sensor-Based Flow Control MPPT Strategy

This section describes the control strategy proposed in this manuscript. As has been mentionedbefore, the objective pursued in this paper consists in the output power maximization by means ofa MPPT strategy. This control technique has already been implemented in other renewable energygeneration plants, such as wind or solar energy, with successful results. Therefore, in case of waveenergy, MPPT should offer similar performance as in already implemented energy systems. However,this strategy must be adapted to wave environment since the behavior of the parameters to becontrolled vary slightly from other systems.

The authors already presented a speed control-based MPPT strategy in [31]. However, in thatcase the optimum rotational speed was empirically obtained from simulations and curve fitting tools.The current research works provides enough mathematical background to display how the optimumrotational speed is obtained.

As it happens in most energy systems where the main motion is the rotational movement of theturbo-generator shaft, the performance of the system can steeply drop according to the rotationalspeed and turbine characteristics. Therefore, in this particular case, MPPT strategy will basically makeuse of the rotational speed control of the turbo-generator.

However, the expression of the optimum rotational speed must be obtained first. In this sense,Equation (6) has been rewritten so as to obtain the mechanical power expression in terms of the torqueratio to the rotational speed.

Sensors 2018, 18, 535 7 of 15

Pt = CtKarωt

(v2

t + (r · ωt)2)

. (7)

Thus, Equation (7) may be derived with respect to the rotational speed, ωt:

∂Pt

∂ωt= Kar

[(v2

t + 3(r · ωt)2)

Ct +(

v2t + (r · ωt)

2)

ωt∂Ct

∂ωt

], (8)

and the singularities of (8) give the expression of the optimum rotational speed, ωopt, according to themaximum power point:

ωopt = −

(v2

t + 3(r · ωopt

)2)

Ctopt(v2

t +(r · ωopt

)2) ∂Ctopt

∂ωt

, (9)

In order to simplify the above equation, Equation (2) has been included in (9), thus obtaining theexpression of ωopt as a function of the optimum flow, ϕopt:

ωopt = −

(φ2

opt + 3)

Ctopt(φ2

opt + 1) ∂Ctopt

∂ωt

. (10)

The turbine usually operates in a stalling-free region, that is to say, the flow coefficient shouldnever overcome the value of 0.3 in normal operating conditions. Accordingly, Equation (3) representedin Figure 3a can be simplified within the operating range:

Ct = −5φ3 + 6φ2 − 0.15φ − 0.02, (11)

whose derivative with respect to ωt must be obtained:

∂Ct

∂ωt=

1ωt

(15φ3 − 12φ2 + 0.15φ

), (12)

and by replacing (11) and (12) in (10) the following expression is obtained:

−10φ5opt + 6φ4

opt − 5.98φ2opt + 0.3φopt + 0.06

15φ5opt − 12φ4

opt + 15.15φ3opt − 12φ2

opt + 0.15φopt= 0. (13)

By solving (13) the value of optimum flow coefficient can be found which, in this particular case,is φopt = 0.1294. Moreover, φopt only depends on Ct, which represents a design feature of Wells turbines,and thus, this value cannot be employed with other turbines.

The equation of mechanical power in (7) can be modified by introducing the flow coefficient termaccording to (2). Thus, Pt can be written as

Pt = CtKar3ω3(

φ2 + 1)

. (14)

Therefore, from (13) and (3) both the flow and torque coefficients are considered unchanging atthe maximum power point, and thus, Equation (14) can be simplified as follows:

Pt = Ktω3, (15)

being Kt = Ctopt Kar3(

φ2opt + 1

).

Accordingly, the aim of the flow controller is to keep the operating point around the optimumflow coefficient according to (13). In this sense, the measurement of the current flow coefficient isneeded as feedback element. This value is estimated from the measurements taken from the pressure

Sensors 2018, 18, 535 8 of 15

drop sensor (see Section 3). Previously, Equation (5) has been modified taking into account the relationbetween φ, and vt in (2):

φ =

(π · dP

CaKaω2 − 1)1/2

, (16)

where the optimum value of the flow coefficient is known at the maximum power point. The blockdiagram of the flow controller is shown in Figure 7, where the estimated flow coefficient from (16) iscompared with φopt obtained from (13).Sensors 2018, 18, x 8 of 14

Figure 7. Flow controller control law scheme.

Therefore, the closed-loop system may be expressed as

2/1

21

)(

)(111

)(1

1

)(

sKC

sdP

sTk

ssT

k

s

aai

p

i

p

opt

,

(17)

so that, referring to (17) in the time domain one has:

t

t

iaa

p

t

i

p

opt d

dTtKC

tdPk

dT

k

t0

00

2/1

2

00

)(1

1)(

)(1

11

)(

.

(18)

The direct chain flow controller is composed of a proportional-integral control law, which is

traditionally used in many control applications. In this case, it provides an adequate performance

with minimum tracking error so as to achieve the pursued objective. However, more advanced

control systems might replace the aforementioned controller.

5. Results

The proposed control scheme in Figure 7 has been implemented in a wave-to-wire plant model

so as to validate the novel MPPT control by means of different simulation case studies.

For this purpose, as has already been mentioned before, a complete wave-to-wire plant model

has been implemented. Figure 8 shows the block diagram of the mentioned plant model, which

basically estimates the air flow through the turbine taking into account different wave parameters at

the surroundings of the breakwater of Mutriku. Once the value of the air flow velocity has been

established, the turbine produces the mechanical torque that makes the generator to rotate. The

rotational speed of the turbo-generator is used as closed-loop element, which is necessary in

addition to the pressure drop measurement from the sensor to estimate the reference rotational

speed.

Figure 8. Common control scheme of OWC-based wave power plant with flow control.

Figure 7. Flow controller control law scheme.

Therefore, the closed-loop system may be expressed as

Φopt(s) =kp

(1 + 1

Tis

)· Ω(s)

1 + kp

(1 + 1

Tis

)(π·dP(s)

CaKaΩ2(s)− 1)1/2 , (17)

so that, referring to (17) in the time domain one has:

φopt(t) =∫ t

0

kp

(1 +

∫ t−τ0

1Ti

dτ0

)1 + kp

(π·dP(t−τ)

CaKaω2(t−τ)

)1/2(1 +

∫ t−τ0

1Ti

dτ0

)ω(τ)dτ. (18)

The direct chain flow controller is composed of a proportional-integral control law, which istraditionally used in many control applications. In this case, it provides an adequate performance withminimum tracking error so as to achieve the pursued objective. However, more advanced controlsystems might replace the aforementioned controller.

5. Results

The proposed control scheme in Figure 7 has been implemented in a wave-to-wire plant model soas to validate the novel MPPT control by means of different simulation case studies.

For this purpose, as has already been mentioned before, a complete wave-to-wire plant modelhas been implemented. Figure 8 shows the block diagram of the mentioned plant model, whichbasically estimates the air flow through the turbine taking into account different wave parameters at thesurroundings of the breakwater of Mutriku. Once the value of the air flow velocity has been established,the turbine produces the mechanical torque that makes the generator to rotate. The rotational speed ofthe turbo-generator is used as closed-loop element, which is necessary in addition to the pressure dropmeasurement from the sensor to estimate the reference rotational speed.

Sensors 2018, 18, 535 9 of 15

Sensors 2018, 18, x 8 of 14

Figure 7. Flow controller control law scheme.

Therefore, the closed-loop system may be expressed as

2/1

21

)(

)(111

)(1

1

)(

sKC

sdP

sTk

ssT

k

s

aai

p

i

p

opt

,

(17)

so that, referring to (17) in the time domain one has:

t

t

iaa

p

t

i

p

opt d

dTtKC

tdPk

dT

k

t0

00

2/1

2

00

)(1

1)(

)(1

11

)(

.

(18)

The direct chain flow controller is composed of a proportional-integral control law, which is

traditionally used in many control applications. In this case, it provides an adequate performance

with minimum tracking error so as to achieve the pursued objective. However, more advanced

control systems might replace the aforementioned controller.

5. Results

The proposed control scheme in Figure 7 has been implemented in a wave-to-wire plant model

so as to validate the novel MPPT control by means of different simulation case studies.

For this purpose, as has already been mentioned before, a complete wave-to-wire plant model

has been implemented. Figure 8 shows the block diagram of the mentioned plant model, which

basically estimates the air flow through the turbine taking into account different wave parameters at

the surroundings of the breakwater of Mutriku. Once the value of the air flow velocity has been

established, the turbine produces the mechanical torque that makes the generator to rotate. The

rotational speed of the turbo-generator is used as closed-loop element, which is necessary in

addition to the pressure drop measurement from the sensor to estimate the reference rotational

speed.

Figure 8. Common control scheme of OWC-based wave power plant with flow control. Figure 8. Common control scheme of OWC-based wave power plant with flow control.

In order to operate at the maximum power point, it is first necessary to determine the value of therotational speed reference for the turbo-generator system. Such a reference speed, ωref, is establishedbased on the MPPT strategy. In this sense, the relation between ωref and the pressure drop, dP, must beoptimum so as to guarantee a maximum transmission of the mechanical torque of the turbine to theturbo-generator shaft. Besides, due to the continuous changes in the sea conditions the pressure dropin the turbine varies constantly, as can be seen in Figure 6. Hence, the control system is beholden to setthe corresponding ωref for each incident wave.

In order to carry out the experiments, random data regarding the wave amplitudes and periodsand corresponding to different sea conditions during five minutes has been used. On the other hand,the parameters used for the OWC chamber, Wells turbine and the induction generator are similar toMutriku and summarized in Table 1.

Table 1. OWC chamber, Wells turbine and generator parameters.

OWC Chamber and Wells Turbine

w Chamber width 4.5 ml Chamber length 4.3 m

D Air duct diameter 0.75 mρ Air density 1.19 kg·m−3

b Blade width 0.21 mlt Blade length 0.165 mn Number of blades 5r Turbine radius 0.375 m

Induction Generator

Snom Apparent power 19.892 kVAcos ϕ Power factor 0.93Vnom Nominal voltage 560 VrmsFnom Nominal frequency 50 Hz

Rs Stator resistance 0.5746 ΩLls Stator inductance 746.3 µHRr Rotor resistance 0.2974 ΩLlr Rotor inductancia 4.183 mHLm Mutual inductance 129.5 mHp Number of poles 2J Inertia 0.55 kg·m2

Sensors 2018, 18, 535 10 of 15

Three case studies have been implemented in order to compare the improvement introducedby the proposed control strategy. In this sense, the first case study considers an uncontrolled plant,where the turbo-generator reaches rotational speeds near the synchronous speed when the generatoris connected directly to the grid, as Figure 9 shows. The second case study employs a traditionalPI control scheme to implement the speed control strategy as in [31]. To conclude, the third casestudy uses the flow controller and pressure sensors described in this manuscript so as to implementMPPT control by setting an optimal rotational speed, and thus, maximize the supplied power. Bothcontrollers show a similar performance. Nevertheless, it can be seen that in case of the flow controlthe rotational speed decreases faster when the wave recedes, so that it improves the efficiency of theconverter, as it will be demonstrated in this section. Thereby, it has been possible to analyze both thecorrect performance of the proposed control strategy and the benefits introduced by it with respect toa PI-based speed controller and an uncontrolled plant.

Figure 10 shows the comparison of the flow coefficient among the uncontrolled plant, PI-basedspeed controller and flow controller. In the case of uncontrolled plant, it can be seen that some wavesproduce values of the flow coefficient beyond the stalling threshold. This means that the turbine stepsinto stall, so that the supplied power is lower since the efficiency of the turbo-generator drops at thesevalues. On the other hand, in both controllers the flow coefficient remains below the threshold valuesalmost all the time. Therefore, the controller not only guarantees the stalling behavior avoidance, butalso improves the power level supplied to the grid.

Regarding the pressure drop in the turbine, the only conclusion that can be taken is that thecontrolled case produces larger pressure drops since it simply operates at higher rotational speeds.Figure 11 shows the pressure drop in both controlled and uncontrolled cases.

Finally, the benefits introduced by the proposed controller in terms of generated power havebeen compared, so that the improvements introduced by the novel control method can be estimated.In this sense, it can be seen in Figure 12 that with the proposed controller the supplied power increasessignificantly in comparison with the uncontrolled plant. Especially during high waves, 50 kW peaksare obtained in the controlled case, while the uncontrolled case is only able to produce 15 kW, only30% of available power.

Sensors 2018, 18, x 10 of 14

Regarding the pressure drop in the turbine, the only conclusion that can be taken is that the

controlled case produces larger pressure drops since it simply operates at higher rotational speeds.

Figure 11 shows the pressure drop in both controlled and uncontrolled cases.

Finally, the benefits introduced by the proposed controller in terms of generated power have been

compared, so that the improvements introduced by the novel control method can be estimated. In this

sense, it can be seen in Figure 12 that with the proposed controller the supplied power increases

significantly in comparison with the uncontrolled plant. Especially during high waves, 50 kW peaks

are obtained in the controlled case, while the uncontrolled case is only able to produce 15 kW, only

30% of available power.

Comparing the flow controller with the PI-based speed controller, as has been mentioned

above, the latter always tries to keep the rotational speed of the generator in the maximum power

point, even there is no torque applied in the turbo-generator shaft. The problem in this case is that

during the period between the incoming and outgoing waves the airflow through the turbine is

practically null. Therefore, since the turbine does not apply any torque, the generator must take

energy from the grid to maintain the rotational speed, as can be seen in Figure 12b. This aspect has

been considerably improved with the flow controller, since the new control method is able to follow

the variations of the pressure drop, and thus the torque, and to decelerate when there no torque is

applied. Hence, the efficiency is improved as the generator does not require to be supplied from the

power grid.

In terms of power, the maximum power reached by both controllers is similar. Nevertheless, 5

min average power produced by both PI-based speed controller and flow controller has been

compared in order to confirm the abovementioned improvement. In this sense, simulations in Figure

12 show that the former controller produces 7.96 kW of average power, while the latter is able to

produce 8.82 kW in the same sea conditions. Therefore, by means of the flow control strategy the

output power has been increased almost in 1 kW in a 5 min period. This means that the conversion

efficiency has been improved by 9.8% in this particular case.

The simulation results also demonstrate that with the new control scheme the efficiency of the

system is improved with respect the controllers implemented by the authors in other works. The

previous speed control tried to keep the rotational speed in the maximum power point even when

there was no torque applied in the turbo-generator shaft during the period between the incoming

and outgoing wave. Therefore, the generator used to take energy from the grid to maintain the

rotational speed. This aspect has been considerably improved with the flow controller, since the new

control method is able to follow the variations of the pressure drop, and thus the torque, and to

decelerate when there is no applied torque. Hence, the efficiency is improved as the generator is not

supplied from the power grid.

Figure 9. Turbine rotational speed, ω (rad/s). (a) Uncontrolled plan; (b) PI-based speed control; (c)

Flow Control.

Figure 9. Turbine rotational speed, ω (rad/s). (a) Uncontrolled plan; (b) PI-based speed control;(c) Flow Control.

Sensors 2018, 18, 535 11 of 15Sensors 2018, 18, x 11 of 14

Figure 10. Flow coefficient, φ. (a) Uncontrolled plant; (b) PI-based speed control; (c) Flow Control.

Figure 11. Pressure drop, dP (Pa). (a) Uncontrolled plant; (b) PI-based speed control; (c) Flow

Control.

Figure 12. Supplied power, P (W). (a) Uncontrolled plant; (b) PI-based speed control; (c) Flow Control.

6. Conclusions

In this paper, a new sensor-based flow control MPPT strategy applied to OWC-based wave

energy system has been presented. In order to achieve the pursued objective, different pressure

sensors have been installed. The first sensor has been used to measure the OWC chamber pressure,

whereas the second measures the pressure drop along the turbo-generator. In this sense, a MPPT

Figure 10. Flow coefficient, ϕ. (a) Uncontrolled plant; (b) PI-based speed control; (c) Flow Control.

Sensors 2018, 18, x 11 of 14

Figure 10. Flow coefficient, φ. (a) Uncontrolled plant; (b) PI-based speed control; (c) Flow Control.

Figure 11. Pressure drop, dP (Pa). (a) Uncontrolled plant; (b) PI-based speed control; (c) Flow

Control.

Figure 12. Supplied power, P (W). (a) Uncontrolled plant; (b) PI-based speed control; (c) Flow Control.

6. Conclusions

In this paper, a new sensor-based flow control MPPT strategy applied to OWC-based wave

energy system has been presented. In order to achieve the pursued objective, different pressure

sensors have been installed. The first sensor has been used to measure the OWC chamber pressure,

whereas the second measures the pressure drop along the turbo-generator. In this sense, a MPPT

Figure 11. Pressure drop, dP (Pa). (a) Uncontrolled plant; (b) PI-based speed control; (c) Flow Control.

Comparing the flow controller with the PI-based speed controller, as has been mentioned above,the latter always tries to keep the rotational speed of the generator in the maximum power point,even there is no torque applied in the turbo-generator shaft. The problem in this case is that duringthe period between the incoming and outgoing waves the airflow through the turbine is practicallynull. Therefore, since the turbine does not apply any torque, the generator must take energy from thegrid to maintain the rotational speed, as can be seen in Figure 12b. This aspect has been considerablyimproved with the flow controller, since the new control method is able to follow the variations ofthe pressure drop, and thus the torque, and to decelerate when there no torque is applied. Hence,the efficiency is improved as the generator does not require to be supplied from the power grid.

In terms of power, the maximum power reached by both controllers is similar. Nevertheless, 5 minaverage power produced by both PI-based speed controller and flow controller has been compared inorder to confirm the abovementioned improvement. In this sense, simulations in Figure 12 show thatthe former controller produces 7.96 kW of average power, while the latter is able to produce 8.82 kW

Sensors 2018, 18, 535 12 of 15

in the same sea conditions. Therefore, by means of the flow control strategy the output power hasbeen increased almost in 1 kW in a 5 min period. This means that the conversion efficiency has beenimproved by 9.8% in this particular case.

The simulation results also demonstrate that with the new control scheme the efficiency ofthe system is improved with respect the controllers implemented by the authors in other works.The previous speed control tried to keep the rotational speed in the maximum power point even whenthere was no torque applied in the turbo-generator shaft during the period between the incoming andoutgoing wave. Therefore, the generator used to take energy from the grid to maintain the rotationalspeed. This aspect has been considerably improved with the flow controller, since the new controlmethod is able to follow the variations of the pressure drop, and thus the torque, and to deceleratewhen there is no applied torque. Hence, the efficiency is improved as the generator is not suppliedfrom the power grid.

Sensors 2018, 18, x 11 of 14

Figure 10. Flow coefficient, φ. (a) Uncontrolled plant; (b) PI-based speed control; (c) Flow Control.

Figure 11. Pressure drop, dP (Pa). (a) Uncontrolled plant; (b) PI-based speed control; (c) Flow

Control.

Figure 12. Supplied power, P (W). (a) Uncontrolled plant; (b) PI-based speed control; (c) Flow Control.

6. Conclusions

In this paper, a new sensor-based flow control MPPT strategy applied to OWC-based wave

energy system has been presented. In order to achieve the pursued objective, different pressure

sensors have been installed. The first sensor has been used to measure the OWC chamber pressure,

whereas the second measures the pressure drop along the turbo-generator. In this sense, a MPPT

Figure 12. Supplied power, P (W). (a) Uncontrolled plant; (b) PI-based speed control; (c) Flow Control.

6. Conclusions

In this paper, a new sensor-based flow control MPPT strategy applied to OWC-based wave energysystem has been presented. In order to achieve the pursued objective, different pressure sensors havebeen installed. The first sensor has been used to measure the OWC chamber pressure, whereas thesecond measures the pressure drop along the turbo-generator. In this sense, a MPPT control method hasbeen implemented so as to maximize the generated power, and thus, to improve the system efficiency.The development of a wave-to-wire plant model has also been carried out and parameterized withmeasured variables and the real parameters of Mutriku Wave Power Plant. The proposed controlscheme has been implemented within the model previously mentioned. The required referencerotational speed of the turbo-generator to maximize the output power has been determined by meansof the established flow coefficient control law. The setting of the reference speed is thereby carried outaccording to the ratio between the measured pressure drop and the rotational speed of the turbine.

The results demonstrate that the proposed control method can be successfully implementedin OWC-based wave energy device and that the system accurately follows the rotational speedreference established by the pressure sensor-based flow control law so that the efficiency of the systemis improved.

Sensors 2018, 18, 535 13 of 15

Acknowledgments: This work was supported in part by the University of the Basque Country (UPV/EHU)through Project PPG17/33, by the MINECO through the Research Project DPI2015-70075-R (MINECO/FEDER,EU) and by the Basque Government through Elkartek. The authors would like to thank the collaboration ofthe Basque Energy Agency (EVE) through Agreement UPV/EHUEVE23/6/2011, the Spanish National FusionLaboratory (EURATOM-CIEMAT) through Agreement UPV/EHUCIEMAT08/190 and EUSKAMPUS – Campusof International Excellence. They would also like to thank Yago Torre-Enciso and Olatz Ajuria from EVE fortheir collaboration and help. The authors would also like to thank the anonymous reviewers that have helped toimprove the initial version of the manuscript.

Author Contributions: Jon Lekube developed the control system and carried out the simulations and wrote themanuscript. Aitor J. Garrido and Izaskun Garrido contributed with the main concept, materials, and editing andrevision. Erlantz Otaola managed data collected from sensors and developed part of the model. Javier Masedaprovided important advice and guidance.

Conflicts of Interest: The authors declare no conflict of interest.

Abbreviations

t, c Time and propagation speed.a, T Wave amplitude and period.w, l Capture chamber width and length.vt, dP Airflow speed and pressure drop.ρ Air density.D, r, at Turbine diameter, radius and area.b, lt Blade span and chord.n Number of blades.φ, Ca, Ct Flow, power and torque coefficients.ωt, Tt, Pt Rotational speed, torque and power.AcronymsEVE Ente Vasco de la EnergíaOWC Oscillating Water Column.MPPT Maximum Power Point Tracking.PLC Programmable Logic Controller.OPC OLE for Process Control.SCADA Supervisory Control and Data Acquisition.

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